1 / 28

Cosmological Parameters with Gravitational Lens systems from the SDSS

Cosmological Parameters with Gravitational Lens systems from the SDSS. Du-Hwan Han & Myeong-Gu Park Kyungpook National University Department of Astronomy and Atmospheric Sciences. INTRODUCTION. Gravitational lens. Deflection of light ray by gravitational fields of massive objects.

mhallman
Download Presentation

Cosmological Parameters with Gravitational Lens systems from the SDSS

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Cosmological Parameters with Gravitational Lens systems from the SDSS Du-Hwan Han & Myeong-Gu Park Kyungpook National University Department of Astronomy and Atmospheric Sciences

  2. INTRODUCTION

  3. Gravitational lens Deflection of light ray by gravitational fields of massive objects.

  4. Gravitational lens • Q0957+561 (SDSS J1001+5553) 1979 Walsh et al. Sloan Digital Sky Survey

  5. Gravitational lens Geometry of gravitational lens

  6. Statistical Analysis • Turner, Ostriker, and Gott (1984)Mean image separation of lens systems have dependence on source redshift. • Gott, Park, and Lee (1989) Calculation of the mean image separation for various cosmology.

  7. MEAN IMAGE SEPARATION

  8. Mean Image Separation Gott, Park, & Lee, 1989, ApJ, 338, 1 Assumption : using lens model as Singular Isothermal Sphere & homogeneous & isotrophic universe described by • Robertson-Walker Metric • Comoving Distance

  9. Mean Image Separation Gott, Park, & Lee, 1989, ApJ, 338, 1 • Flat Universe • Open Universe • Closed Universe

  10. Cosmological Models • empty universe • open universe • flat universe • closed universe • closed universe Park & Cott, 1997 Park, 1998

  11. LENS SYSTEMS FROM THE SDSS

  12. Candidates for Lens systems from the SDSS The SDSS is completed its 1st of operation. ⇒ ~ 90,000 quasars Candidates selected by lens selection algorithm (Oguri et al.). ⇒ 171 candidates 171

  13. Candidates for Lens systems from the SDSS The SDSS is completed its 1st of operation. ⇒ ~ 90,000 quasars Candidates selected by lens selection algorithm (Oguri, et. al.). ⇒ 171 candidates Select 76 candidates between 1” and 5” 76

  14. Candidates for Lens systems from the SDSS The SDSS is completed its 1st of operation. ⇒ ~ 90,000 quasars Candidates selected by lens selection algorithm (Oguri, et. al.). ⇒ 171 candidates Select 76 candidates between 1” and 5” Oguri, et. al., 2006, AJ, 132, 999

  15. Candidates for Lens systems from the SDSS 76 candidates

  16. CURVATURE TEST

  17. Curvature Test Candidates for Lens systems Mean image separation

  18. Curvature Test • Spearman Rank Correlation Test • Test of the strength of a correlation.Using the rank of two quantities. =+1 positive correlation correlation coefficient = 0 no correlation =-1 negative correlation • ‘Normalized’⇒ Observed image separation divide by mean image separation of cosmological model. • Null hypothesisthere is no correlation between ‘normalized’ image separation versus source redshift.

  19. Curvature Test

  20. Likelihood Map < 0.01 0.01 No Big Bang 0.05 No Big Bang 0.01 0.05 0 ≤ Ω ≤ 3 0 ≤ ΩΛ ≤ 3 0.32 0.32 0.70 k=0 > 0.32 0.70 K=0

  21. Ωm- ΩΛ TEST

  22. Lensing Probability • Probability distribution for image separation • For elliptical (i=E) and lenticular (i=SO) galaxies, • For spiral (i=S) galaxies, Where, Ai=0.12, 0.19, 0.69 for E,S0,S galaxy type and

  23. Ωm- ΩΛTEST • Maximum Likelihood Methodis a useful tool to set constraints on parameters of the statistical model with a given data set • Likelihood function • For the JVAS/CLASS sample • For the SDSS sample

  24. The JVAS/CLASS sample ▬ 99% CL ▬ 95% CL ▬ 68% CL No Big Bang

  25. The SDSS sample ▬ 99% CL ▬ 95% CL ▬ 68% CL No Big Bang

  26. The SDSS sample ▬ 99% CL ▬ 95% CL ▬ 68% CL No Big Bang

  27. SUMMARY

  28. Summary • Calculation of the mean image separation as a function of source redshift for various cosmological models • Distribution of Candidates for lens systems from the SDSS show slightly positive correlation or do not show any correlation. • Curvature TestSpearman test shows the curvature of the universe is ‘0’, ‘negative’ or ‘not-excessively’ positive. • Ωm-ΩΛ TestCalculated the probability distribution and maximum likelihoodwith the JVAS/CLASS sample and the SDSS sample.

More Related